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ap statistics chapter 7, Study Guides, Projects, Research of Mathematics

Mathematics

ap statistics study guide chapter 7

Typology: Study Guides, Projects, Research

2023/2024

Uploaded on 02/29/2024

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Test 7B AP Statistics Name:
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1. In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is
examined. Forty percent of the trees show some signs of damage. Which of the following
statements is correct?
(a) 40% is a parameter
(b) 40% is a statistic
(c) 40% of all trees in the forest show some signs of damage
(d) More than 40% of the trees in the forest show some signs of damage
(e) Less than 40% of the trees in the forest show some signs of damage
2. The sampling distribution of a statistic is
(a) the probability that we obtain the statistic in repeated random samples.
(b) the mechanism that determines whether randomization was effective.
(c) the distribution of values taken by a statistic in all possible samples of the same sample
size from the same population.
(d) the extent to which the sample results differ systematically from the truth.
(e) the distribution of values in a sample of size n from the population
3. A statistic is said to be unbiased if
(a) the survey used to obtain the statistic was designed so as to avoid even the hint of racial
or sexual prejudice.
(b) the mean of its sampling distribution is equal to the true value of the parameter being
estimated.
(c) both the person who calculated the statistic and the subjects whose responses make up the
statistic were truthful.
(d) the value from any sample is equal to the parameter being estimated.
(e) it is used for honest purposes only.
4. Which of the following distributions has a mean that varies from sample to sample?
I. The population distribution
II. The distribution of sample data
III. The sampling distribution
(a) I only
(b) II only
(c) III only
(d) II and III
(e) all three distributions
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Test 7B AP Statistics Name:

Part 1: Multiple Choice. Circle the letter corresponding to the best answer.

1. In a study of the effects of acid rain, a random sample of 100 trees from a particular forest is examined. Forty percent of the trees show some signs of damage. Which of the following statements is correct? (a) 40% is a parameter (b) 40% is a statistic (c) 40% of all trees in the forest show some signs of damage (d) More than 40% of the trees in the forest show some signs of damage (e) Less than 40% of the trees in the forest show some signs of damage 2. The sampling distribution of a statistic is (a) the probability that we obtain the statistic in repeated random samples. (b) the mechanism that determines whether randomization was effective. (c) the distribution of values taken by a statistic in all possible samples of the same sample size from the same population. (d) the extent to which the sample results differ systematically from the truth. (e) the distribution of values in a sample of size n from the population 3. A statistic is said to be unbiased if (a) the survey used to obtain the statistic was designed so as to avoid even the hint of racial or sexual prejudice. (b) the mean of its sampling distribution is equal to the true value of the parameter being estimated. (c) both the person who calculated the statistic and the subjects whose responses make up the statistic were truthful. (d) the value from any sample is equal to the parameter being estimated. (e) it is used for honest purposes only. 4. Which of the following distributions has a mean that varies from sample to sample? I. The population distribution II. The distribution of sample data III. The sampling distribution (a) I only (b) II only (c) III only (d) II and III (e) all three distributions

5. You take a sample of size 25 from a very large population in which the true proportion is

p 0.1, thus violating the condition that np 10 and n  1  p 10. Which statement below

best describes what you know about the sampling distribution of p ˆ^?

6. The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that (a) as we look at more and more bulbs, their mean burnout time gets ever closer to the

mean for all bulbs of this type.

(b) the mean burnout time for any number of bulbs has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs. (c) the mean burnout time for any number of bulbs has a distribution that is close to Normal. (d) the mean burnout time for a large number of bulbs has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs. (e) the mean burnout time for a large number of bulbs has a distribution that is close to Normal.

7. You take an SRS of size 500 from the 37,000 students at Purdue University and measure individual’s heights. You then take an SRS of size 500 from the 4,400,000 adults in the state of Indiana and measure their heights. Assuming the standard deviation of individual heights in the two populations is the same, the standard deviation of the sampling distribution of mean heights for the Indiana sample is (a) approximately the same as for the Purdue sample because both are samples of size 500. (b) smaller than for the Purdue sample because the population of Indiana is much larger. (c) larger than for the Purdue sample because the population of Indiana is much larger. (d) larger, because the Indiana sample is smaller relative to the population from which it’s been taken. (e) either larger or smaller than for the Purdue sample because it varies from sample to sample.

Part 2: Free Response

Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations.

11. The weight of the eggs produced by a certain breed of hen is Normally distributed with mean 65 grams (g) and standard deviation 5 g. (a) Calculate the probability that a randomly selected egg weighs between 62.5 g and 68. g. Show your work. (b) Think of cartons of such eggs as SRSs of size 12 from the population of all eggs. Calculate the probability that the mean weight of the eggs in a carton falls between 62.5 g and 68.75 g. Show your work. (c) Did you need to know that the population distribution of egg weights was Normal in order to complete parts (a) or (b)? Justify your answer.

12. Companies are interested in the demographics of those who listen to the radio programs they sponsor. A radio station has determined that only 20% of listeners phoning in to a morning talk program are male. The station management wonders if adding a male host to the program will increase the proportion of callers who are male. After adding the male host, the station records the gender of 200 people who phone in to the program during a particular week. The station is willing to view these 200 callers as an SRS from the population of all those who call in to this program. (a) For the moment, assume that the addition of the male host has no effect on the proportion of callers who are male. If p ˆ is the proportion of callers in the sample who are male, what are the mean and standard deviation of the sampling distribution of p ˆ? (b) What assumption are you making when you use the formula for the standard deviation of p ˆ in this setting? (c) In fact, during this particular week, 50 of the 200 callers were male. Does this provide sufficient evidence to suggest that the proportion of male callers has increased from 20%? Support your answer with an appropriate probability calculation.